The talk will explain how Grothendieck toposes can be effectively used as ‘bridges’ for transferring ideas and results across different mathematical theories. The interest of these general techniques is that they allow one to discover in classical domains new results which are established by topos-theretic means but whose statement does not involve toposes.

By way of example, these general methods will be illustrated by a topos-theoretic reinterpretation and generalisation of Stone-type dualities in topology.